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Conformal symmetries of a sphere are generated by the inversion in all of its hyperspheres. On the other hand, Riemannian isometries of a sphere are generated by inversions in geodesic hyperspheres (see the Cartan–Dieudonné theorem.) The Euclidean sphere can be mapped to the conformal sphere in a canonical manner, but not vice versa.
Indiana University Indianapolis Type Public research university Established July 1, 2024 ; 6 months ago (2024-07-01) Parent institution Indiana University Academic affiliations Space-grant Endowment $1.15 billion (2020) Chancellor Latha Ramchand Academic staff Over 2,500 Students 29,390 (Fall 2020) Undergraduates 20,441 (Fall 2020) Postgraduates 8,171 (Fall 2020) Location Indianapolis, Indiana ...
The stereographic projection maps the -sphere onto -space with a single adjoined point at infinity; under the metric thereby defined, {} is a model for the -sphere. In the more general setting of topology , any topological space that is homeomorphic to the unit n {\displaystyle n} -sphere is called an n ...
A sphere has 2/3 the volume and surface area of its circumscribing cylinder. A sphere and cylinder were placed on the tomb of Archimedes at his request. Archimedes (c. 287 BCE – c. 212 BCE), a colorful figure about whom many historical anecdotes are recorded, is remembered along with Euclid as one of the greatest of ancient mathematicians.
A sphere (from Greek σφαῖρα, sphaîra) [1] is a geometrical object that is a three-dimensional analogue to a two-dimensional circle.Formally, a sphere is the set of points that are all at the same distance r from a given point in three-dimensional space. [2]
In geometry, many uniform tilings on sphere, euclidean plane, and hyperbolic plane can be made by Wythoff construction within a fundamental triangle, (p q r), defined by internal angles as π/p, π/q, and π/r. Special cases are right triangles (p q 2).
Indiana University has two core campuses, five regional campuses, and two regional centers under the administration of IU Indianapolis. Indiana University Bloomington (IU Bloomington) is the flagship campus of Indiana University. [ 3 ]
The two institutions jointly operated Indiana University–Purdue University Indianapolis (IUPUI) until its dissolution in 2024. [356] IU Indianapolis is an urban research university that enrolls about 25,000 students in 330 different bachelor's